The invention relates to wireless communications and, more particularly, to space time coding techniques for wireless communications.
Wireless communications using multiple transmit and receive antennas can increase the multiplexing gain (i.e., symbol throughput) and diversity gain (i.e., robustness) of communication systems in fading channels. It has been shown that for any given number of antennas there is a fundamental tradeoff between these two goals. A practical coding technique which maximizes these two goals is referred to as lattice space time (LAST) coding, which can be efficiently decoded with receivers of lower complexity than the maximum likelihood decoder. See, e.g., H. El Gamal, G. Caire, M. O. Damen, “Lattice Coding and Decoding Achieve the Optimal Diversity-Multiplexing Tradeoff of MIMO Channels,” IEEE Transactions on Information Theory, Vol. 50, No. 6 (June 2004). Unfortunately, the diversity-multiplexing tradeoff frame-work does not say anything about the coding gain or error rate at the signal-to-noise (SNR) ratios of interest. That is, for two LAST code designs with the same tradeoff, different error rate performance can be obtained in the signal-to-noise ratios of interest. Finding the LAST code within a family of LAST codes which minimizes the error rate is complicated by the lack of a closed-form expression for the error rate. Prior art LAST code designs disclose lattices which are error rate optimal only for the single antenna AWGN channel and the maximum likelihood decoder. These lattices, however, are not necessarily error optimal for the general MIMO fading channel or for other receiver structures.
Accordingly, there is a need for a new approach to the construction of lattice space-time codes that can optimize error rates across different decoder structures.